Transport Properties of Superfluid 3He

Abstract

The coefficients of first viscosity, thermal conductivity and spin diffusion for the super­ fluid 'He are calculated from the kinetic equation by solving the integral equation firising from the collision integral. The temperature dependences of these coefficients are computed near the transition temperature and the absolute, zero temperature, allowing the energy gap to be anisotropic and isotropic as well as non-unitary for the spin diffusion problem and are compared with experiments for the viscosity and the thermal conductivity, showing a reasonably good agreement. § I. Introduction Recently the experiments of Alvesalo et al_1J,2l and Wheatley et al,Bl have disclosed the behavior of the viscosity and thermal conductivity of the superfluid sHe for the· A- and B-phases. The theoretical calculation for them are performed by Shumeiko4l and Seiden5l for the isotropic superfluid, the latter using the low temperature approximation and disagreeing with the experiment. In this work we treat the transport coefficients of a Fermi superfluid in ~hich a quasi-particle may have an anisotropic energy gap, solving the kinetic equation with a collision integral. We compute the temperature dependence of the coefficients of the viscosity, thermal conductivity and spin diffusion. The superfluidity of liquid sHe predicted by one of us (T .S.) 6l has been discoverd by the experiments~l in 1972 by the anomaly along the melting curve. NMR experiments 8l established that the A-phase of liquid 3He is the Cooper pair of the equal spin state (ESP) of the odd orbital angular momentum. The experiment of static magnetic susceptibility 9J,lOJ showed. that the B-phase looks like due to the Cooper pair which contains the antiparallel spin state. Soda and Yamazaki11l developed a phenomenological, theory to regard the A-phase as . a superfluid of the F orbital angular momentum ESP Cooper pair and the B-phase as one of the singlet D orbital angular momentum Cooper pair along this line. Meanwhile the spherical triplet state with the same orbital angular momentum ' as the Cooper pair of the A-phase is now favoured by the experiments12l of the longitudinal NMR and low-temperature magnetic susceptibility in the B-phase. We present a theory of transport coefficient for the superfluid in this paper as an extension of our theoretic!fl investigation of the superfluid sHe. The method we use here is the extension of tpe Landau approach13l of normal Fermi liquid to the superfluid of quasi-particles, where the effective